Summary: A Pension Fund Model with
Surplus: an Infinite Dimensional
Stochastic Control Approach
Salvatore Federico
Preprint di Matematica ­ N. 8
Settembre 2007
A Pension Fund Model with Surplus: an Infinite
Dimensional Stochastic Control Approach
Salvatore Federico
September 10, 2007
1 Introduction
In the paper [6] the authors propose and study a continuous time stochastic
model of optimal allocation for a defined contribution pension fund with mini-
mum guarantee.
Their target is to maximize the expected utility from current wealth over
an infinite horizon, whereas usually portfolio selection models for pension funds
maximize the expected utility from final wealth over a finite horizon (the retire-
ment time). In this model the dynamics of wealth takes directly into account the
flows of contributions and benefits; moreover the level of wealth is constrained
to stay above a solvency level. The fund manager can invest in a riskless asset